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Showing posts from September, 2014

Third expedition La Salle expeditions

native americans guide french explorers through indiana depicted maurice thompson in stories of indiana. in late 17th century, la salle began process of expanding , securing fur trade building series of forts , line of communications montreal upper great lakes , ohio valley , mississippi regions. in 1673 built fort frontenac @ cataraqui (now kingston) on lake ontario. in 1679 built fort conti @ mouth of niagara river on lake ontario. near fort constructed sailing ship named le griffon , used explore of great lakes. voyaged far modern green bay, wisconsin in following summer set trading post. region still locked in beaver wars , new route on lakes allowed french bypass dangerous countryside , trade tribes beyond front lines of war. while remained @ post, sent 2 men indian guide westward in search of mississippi river. 2 men located falls of st. anthony before returning. in september 1679 began return trip niagara stopped @ mouth of st. joseph river on east shore of lake michigan. paddle

Soundtrack Blade II

blade ii: soundtrack soundtrack film, blade ii. released on march 19, 2002 through immortal records , virgin records, , featured collaborations between hip hop artists , electronic artists. similar other releases immortal records such soundtracks films judgment night (1993) featured collaborations between rock , hip hop performers, , on soundtrack film adaptation spawn (1997) featured collaborations between rock , electronic artists. allmusic gave positive review, praising collaborations more others. this soundtrack appeared on 4 different billboard charts. blade ii reached no. 26 on billboard 200 chart. track listing

Adoration and Benediction outside of the Liturgy Eucharist in the Catholic Church

host displayed in monstrance, flanked candles being adored kneeling altar server exposition of eucharist display of consecrated host on altar in monstrance. rites involving exposition of blessed sacrament benediction of blessed sacrament , eucharistic adoration. adoration of eucharist sign of devotion , worship of christ, believed present. host reserved in tabernacle after mass , displayed in monstrance during adoration. catholic devotion, eucharistic adoration , meditation more merely looking @ host, continuation of celebrated in eucharist. theological perspective, adoration form of latria, based on tenet of presence of christ in blessed host. christian meditation performed in presence of eucharist outside mass called eucharistic meditation. has been practiced saints such peter julian eymard, jean vianney , thĆ©rĆØse of lisieux. authors such venerable concepcion cabrera de armida , blessed maria candida of eucharist have produced large volumes of text based on eucharistic meditations. w

Layout and geomantic positioning Buddhist temples in Japan

part of tōshōdai-ji s garan (left right, kondō, kōdō, korō , raiō) buddhist temple complexes consist of number of structures arranged according concepts or guidelines. the arrangement of major buildings (garan haichi (ä¼½č—é…ē½®)) changed on time. pattern had gate, tower, kondō , kodō in straight line south north. corridors extended east , west flanks of gate, turned north, , joined north of kōdo, forming cloister around pagoda , major halls. pattern, typified shitennō-ji in osaka, came china via baekje; chinese style of buddhist temples, though altered china via korean peninsula, based on of chinese palaces, , evident in many of basic design features remain today in temples of 3 countries. a buddhist temple complex in japan follows pattern of series of sacred spaces encircling courtyard, , entered via set of gates. these gates typically have pair of large guardian statues, called niō. in addition, many of more important or powerful temples built in locations favorable according precepts of

Japan Evolution of the Dutch Empire

firando (1609–1641)* deshima (1641–1853)* dutch maintained trading post @ hirado, 1609 1641. japanese granted dutch trade monopoly in japan 1641 1853, solely on deshima, artificial island off coast of nagasaki. during period europeans allowed japan. chinese , korean traders still welcome, though restricted in movements.

History Budgewoi, New South Wales

1 history 1.1 surrounding areas 1.2 schools 1.3 churches history in 1827, john slade offered grant of 640 acres (2.6 km) appears not have taken offer. on 11 august 1843, robert henderson granted 640 acres (2.6 km) in known budgewoi, had dairy. in 1856 henderson holdings purchased john hargraves built noraville . wollombi aboriginal tribe members known have worked on property. sources state hargraves befriended tribe members. cattle grazed far buff point , elizabeth bay. norah head lighthouse built , opened in 1903 after vessel wreckages. originally used grazing cattle , agriculture, 1930s budgewoi becoming known holiday destination , families come sydney camp on weekends , during holidays. however, getting area not easy did not become popular other places on central coast. surrounding areas chinese fishermen worked tuggerah lakes area in late 1850s, in particular, known canton beach @ toukley. while not confirmed, believed name derived from. base catching , curing fish shipped queen

Book Reviews and Critical Acclaim David Gussak

1 book reviews , critical acclaim 1.1 book review 1.2 critical acclaim 1.3 selected bibliography 1.4 references 1.5 external links book reviews , critical acclaim book review van der vennet (2014) reviewed gussak’s book, art on trial: art therapy in capital murder cases. review gave credit gussak bringing notoriety art therapy field moving forensics forefront of art therapy field internally. gussak given acknowledgment becoming expert witness art therapist on capital murder trial. using ethical , legal protocol prescribed american art therapy association (aata) , art therapy credentials board (atcb), gussak able compete @ equal competence level other qualified mental health professionals. gussak used standardized instruments measure defendant kevin ward’s (pseudonym) artwork way of person picking apple tree (ppat), later assessed standardized formal elements art therapy scale (feats). both ppat , feats used tools furnish mental health diagnosis of schizophrenia related disorder accused

Notable alumni Arcadia High School (California)

bruce bochte, professional baseball player (mlb) 1974-86 stacie chan, voice of jade in animated television series jackie chan adventures renee chen, taiwanese singer , songwriter signed warner music jason chen, youtube artist single best friend has gotten on 10 million views scoop deville, hip-hop music producer , rapper, founding member of busy committee, son of rapper kid frost marianne gravatte, model/actress , 1983 playmate of year dave hostetler, professional baseball player 1981-88 mel hutchins, professional basketball player 1951-58 steve kemp, professional baseball player 1977-88 mike lansford, professional football placekicker los angeles rams 1980-90 bruce matthews played football @ arcadia high , @ usc; played in nfl houston oilers/tennessee titans; first-year (inducted in first year of eligibility) hall of famer of 2007 clay matthews played football @ arcadia high , @ usc; played in nfl cleveland browns , atlanta falcons; 4-time pro bowler mirai nagasu, national champion

Infrastructure Visakhapatnam Steel Plant

panorama view of vizag steel plant the prepared coal charge in coal tower drawn charging car on top of batteries , charged ovens per sequence. charged coal gradually heated heating wall of oven in absence of air attain temperature of 1000°-1050 °c @ central axis of coke mass toward end of coking period. coking period specified between 16 hrs , 19 hrs depending on oven condition , production requirement. volatile matter of coal liberated during carbonization collected in gas collecting mains in form of raw coke oven gas passing through stand pipes , direct contact cooling ammonia liquor spray. gas cooled 800 °c drawn coal chemical plant exhauster. residual coke pushed out of oven pusher car through guide coke bucket. red-hot coke taken coke dry cooling plant cooling.there 4 batteries, each having 67 ovens each. each oven can hold 32 tons of dry coal charge. volumetric capacity of each oven 41.6 cum heat carbonation supplied under firing of coke oven gas having cv of 4200 kcal/nm3 of mix

Socialization Athabaskan fiddle

trio playing @ 2011 festival. lineup shown of electric guitar, fiddle , acoustic guitar typical of lineups seen @ festival. since 1983 athabascan fiddle festival or athabascan fiddling festival held annually in november in fairbanks. festival instituted in 1983 alaska state council on arts (asca) , institute of alaska native art , continues vital. festival described testament far-reaching appeal of traditional music , festival features athabaskan , eskimo (yup ik , iƱupiaq) fiddlers. when bill stevens returned alaska in 1982, became instrumental in development of festival. continues participate in annual four-day celebration has become major cultural event people of interior. the november festival carries on tradition of fiddle music bringing bands on state, including few eskimo bands, many of whom save year participate in jubilant event. festival prides on being sober event, people can gather family fun, in safe environment. starting around 2005, festival split 2 venues, 1 featuring f

With Captain Stairs to Katanga Joseph Moloney

the expedition took year round trip base in zanzibar msiri s capital @ bunkeya, stayed 2 months. suffered disease, starvation while, , numerous hardships. quarter of africans , 2 out of 5 europeans died, including captain stairs, moloney spared severe illness. in bunkeya, msiri refused sign treaty accepting leopold s sovereignty , cfs flag, , killed second officer omer bodson had recklessly confronted msiri in situation he, bodson, not control. msiri s people , successor chief, seeing expedition s greater firepower, bowed inevitable , signed treaty. katanga became part of leopold s congo free state, achieved later notoriety colonial slave state. moloney s book has significant omission. evidence of msiri s barbarity , notes placed heads , skulls of executed enemies , miscreants on poles , palisades of boma. article in french published in paris around same time moloney s book in moloney s colleague on expedition, marquis christian de bonchamps, revealed after killing him, cut off msiri

Matches 2016–17 Magyar Kupa (women's handball)

1 matches 1.1 round i 1.2 round ii 1.3 round iii 1.4 round iv 1.5 quarter-finals matches a total of 46 matches take place, starting round on 14 september 2016 , culminating final on 2 april 2017 @ messzi istvĆ”n sports hall in kecskemĆ©t. round i the first round ties scheduled 14 – 21 september 2016. round ii the second round ties scheduled 11 – 19 october 2016. round iii the third round ties scheduled 1 – 13 november 2016. round iv the fourth round ties scheduled 4 january 2017. quarter-finals the quarterfinals ties scheduled 15 february 2017.

Administrative divisions Zigong

sichuan basin satellite view zigong salt museum although region has rich history antiquity, prefecture-level city called zigong modern name. in 1939, 2 older cities combined make zigong - ziliujing (some have romanized name tzeliutsing ) , gongjing named zigong. zigong name combination of both older cities names. today there 4 municipal districts , 2 counties of zigong prefecture. information here presented uses metric system , data 2010 census. both previous cities - gongjing , ziliujing made had become 1 of busiest saltworks (or saltyards called locally) in china - furong saltyard. main products uniquely rich salt called hua salt - dominated salt other sichuan producers , ba salt became popular in other provinces in china.

Accomplishments and influence Carioca

carioca people have invented few sports; famous footvolley. cariocas credited creating bossa nova dance. famous cariocas in film include brazilian bombshell carmen miranda, portuguese woman grew in rio de janeiro. eponymous song 1933, carioca, has become jazz standard. carnaval carioca portuguese name largest brazilian carnival, rio carnival. samba carioca localized style of brazilian samba. there exercise drill used dynamic stretching called carioca. consists of repeating samba dance step.

Members IAMMEDIC

1 members 1.1 enik lin 1.2 danny park 1.3 andre harris 1.4 dj yup members enik lin enik lead vocals, producer, main writer, programming, sequencing, piano, keyboards, guitars, drums, violin, keyboards iammedic. before starting iammedic, lin in band called burning tree project (tragic hero/east west/warner). enik has released 2 singles off forthcoming solo album. danny park danny contributes background vocals , producer. park dj on 1tym danny s (taebin) danny la on mnet (tv channel). park produced mnet s docu-reality tv show alpha girls , ktown night market event in los angeles, california. andre harris also known dre. started rapping @ age of 11, joined several local hip-hop groups. little after, learned play piano jazz player, peter deneff, , songwriter, joseph gallo. played keyboards , vocals burning tree project. in charge of vocals, keyboards , co-writer iammedic. dj yup also known sangyup jeon, yup newest member , official dj iammedic. contributes live dj , live sequencing

Complications Ocean fertilization

1 complications 1.1 outright opposition 1.2 efficiency 1.3 side effects 1.3.1 algal blooms 1.3.2 impact on fisheries 1.3.3 ecosystem disruption 1.3.4 cloud formation complications while manipulation of land ecosystem in support of agriculture benefit of humans has long been accepted (despite side effects), directly enhancing ocean productivity has not. among reasons are: outright opposition according lisa speer of natural resources defense council, “there limited amount of money, of time, have deal problem....the worst possible thing climate change technologies invest in doesn’t work , has big impacts don’t anticipate.” in 2009  aaron strong, sallie chisholm, charles miller , john cullen opined in nature ...fertilizing oceans iron stimulate phytoplankton blooms, absorb carbon dioxide atmosphere , export carbon deep sea — should abandoned. efficiency algal cell chemical composition 106 carbon: 16 nitrogen: 1 phosphorus: 0.0001 iron atoms. in other words, each atom of iron captures 1,06

International affiliations CPA Australia

1 international affiliations 1.1 pakistan 1.2 canada 1.3 europe 1.4 hong kong 1.5 india 1.6 singapore 1.7 sri lanka 1.8 malaysia 1.9 united kingdom 1.10 others international affiliations cpa australia has affiliations range of leading accounting bodies around world, ensure cpas internationally recognized. these include: pakistan the institute of cost & management accountants of pakistan institute of chartered accountants of pakistan pakistan institute of public finance accountants canada certified general accountants canada certified management accountants canada europe chartered institute of public finance , accountancy chartered institute of management accountants cpa ireland: institute of certified public accountants in ireland hong kong hong kong institute of certified public accountants. india institute of chartered accountants of india. singapore institute of singapore chartered accountants. sri lanka institute of chartered accountants of sri lanka. institute of certified man

Episodes All Quiet on the Preston Front

1 episodes 1.1 series one 1.2 series two 1.3 series three episodes three series made. series 2 , 3 title shortened preston front, series became less ta , more personal lives of protagonists. series one series two series three locations although set in lancashire, majority of filming took place, scenes filmed @ locations in midlands, including black country museum.

What is read Torah reading

1 read 1.1 weekly portion 1.2 daily portion 1.3 jewish holidays 1.4 order of precedence special readings what read the cycle of weekly readings fixed. because hebrew calendar varies year year, 2 readings combined entire pentateuch read on course of year. weekly portion on shabbat mornings, weekly torah portion (parashah) read. divided 7 aliyot (see above more on aliyot). daily portion on monday , thursday mornings , on saturday afternoons (except on special days), small section of upcoming week s parashah read, divided 3 aliyot jewish holidays on jewish holidays, reading relates day. example, on passover congregation reads various sections of pentateuch relate holiday. order of precedence special readings when multiple special occasions occur @ same time, there standard order of precedence. speaking, when major jewish holidays occur on shabbat holiday portion read, although divided 7 portions shabbat rather number appropriate holiday — there special reading when shabbat coincides chol

United States v. Cruikshank Second Amendment to the United States Constitution

in reconstruction era case of united states v. cruikshank, 92 u.s. 542 (1875), defendants white men had killed more sixty black people in known colfax massacre , had been charged conspiring prevent blacks exercising right bear arms. court dismissed charges, holding bill of rights restricted congress not private individuals. court concluded, [f]or protection in enjoyment, people must states. the court stated [t]he second amendment...has no other effect restrict powers of national government ...... likewise, court held there no state action in case, , therefore fourteenth amendment not applicable: the fourteenth amendment prohibits state depriving person of life, liberty, or property, without due process of law; adds nothing rights of 1 citizen against another. thus, court held federal anti-ku-klux-klan statute unconstitutional applied in case.

Location Eurovision Song Contest 1979

international convention center, jerusalem – host venue of 1979 contest. located on plateau in judean mountains between mediterranean , dead sea, jerusalem 1 of oldest cities in world. in ancient cuneiform, jerusalem called urusalima , meaning city of peace , during canaanite period (approximately 2400 bc). considered holy 3 major abrahamic religions—judaism, christianity , islam.

Origin 25 Field Artillery

1 origin 1.1 conversion medium regiment 1.2 operations 1.3 traditions 1.3.1 emblem design 1.3.2 commanding officer saber origin this unit formed 25 composite regiment on 17 may 1977 , based in potchefstroom. composite unit, comprised a couple of gun batteries, heavy mortars and, counter artillery locating radar elements.(typically using cymbeline mk1 locating radar) conversion medium regiment by 1984 regiment altered removal of mortar , radar , conversion medium regiment. operations on 3 may 1984 regiment added operational control of far north command. citizen force regiment, primary function artillery support , secondary function infantry. regiment operational in border area zimbabwe in 1980 , in south west africa in 1983. traditions emblem design the regiment had typical artillery tradition , instead of having colours considered cannons colours. unit received ceremonial emblems on 21 september 1984. emblem has traditional artillery background colours of red , dark blue separated gold

Public opinion polls Washington Redskins name controversy

while varying somewhat, national opinion polls consistently indicate majority of general public not advocate name change: 79 percent (april 2013), 60 percent (june 2014), , 71 percent (september 2014). while yielding overall results similar national polls, majority supporting team keeping name, local surveys ask additional questions. in 3 polls, although supported team name, 59 percent, 56 percent, , 53 percent of dc, maryland, , virginia fans said word redskin offensive native americans in @ least contexts. september 2014 national poll found 68 percent think name not disrespectful of native americans, 19 percent shows disrespect, , 9 percent lot disrespectful. 2016 annual nfl poll found significant difference of opinion based upon age , race. older respondents opposed name change, between 18 , 29 (70%) in favor of change. while 77% of white fans believe name should not changed, 38% of african-american , 33% of latino fans agree, change since 2014 poll in there little difference

Church of England List of churches in Oxford

st cross church. christ church cathedral, st aldate s all saints, lime walk, headington holy trinity church, headington quarry pusey house, st giles street st alban martyr, charles street st aldate s, st aldate s street st andrew, st andrew s road, headington st andrew, linton road st barnabas, cardigan street, jericho st bartholomew s chapel, bartlemas, cowley road st clement, marston road st ebbe, pennyfarthing place st francis of assisi, hollow way, cowley st frideswide, botley road st giles, woodstock road st james, beauchamp lane, cowley st john evangelist, iffley road st john evangelist, vicarage road st luke, canning crescent st margaret s, st margaret s road st mary magdalen, magdalen street st mary, bayswater road, barton st mary , st john, cowley road st mary virgin, iffley st matthew, marlborough road st michael , angels, lonsdale road, summertown st michael , angels, marston road, new marston st michael @ northgate, cornmarket street st thomas martyr, becket street univers

Types of lethal alleles Lethal allele

1 types of lethal alleles 1.1 recessive lethals 1.2 dominant lethals 1.3 conditional lethals types of lethal alleles recessive lethals a pair of identical alleles both present in organism results in death of organism referred recessive lethal alleles. though recessive lethals may encode dominant or recessive traits, fatal in homozygous condition. heterozygotes display form of disease phenotype, in case of achondroplasia. 1 mutant lethal allele tolerated, having 2 results in death. in case of homozygous achondroplasia, death invariably occurs before birth or in perinatal period. not heterozygotes recessive lethal alleles show mutant phenotype, case cystic fibrosis carriers. if 2 cystic fibrosis carriers have children, have 25 percent chance of producing offspring having 2 copies of lethal allele, resulting in death of child. another example of recessive lethal allele occurs in manx cat. manx cats possess heterozygous mutation resulting in shortened or missing tail. crosses of 2 heterozy

In Lutheranism The righteous perishes

der gerechte kƶmmt um, chorus appearing in pasticcio passion oratorio 1750s, has german version of isaiah 57:1–2 text. arrangement attributed johann sebastian bach of ssatb setting of tristis est anima mea, motet attributed johann kuhnau. arrangement may have been stand-alone funeral motet.

2010–present Olympiacos F.C.

ernesto valverde kevin mirallas in 2010, evangelos marinakis, successful shipping magnate, bought team sokratis kokkalis. during first year of presidency, marinakis appointed fans favourite ernesto valverde coach (who came second tenure in club) , signed players international pedigree, such albert riera, ariel ibagaza, kevin mirallas, marko pantelić , franƧois modesto. result, olympiacos won greek title 38th time in history, 13 points ahead of second-placed panathinaikos. in 2011–12 season, team s roster strengthened players jean makoun, pablo orbaiz, ivĆ”n marcano, rafik djebbour , djamel abdoun , ernesto valverde coach second straight season, olympiacos had successful campaign both domestically , internationally. won both greek league , greek cup complete 15th domestic double in club s history. in european competitions, olympiacos had solid champions league campaign, having been drawn in group f against arsenal, borussia dortmund , marseille. despite delivering 9 points in group, 2 e

2002.E2.80.9309 .E2.80.93 USC.27s Dominance Notre Dame–USC football rivalry

after beating irish 31 points each of past 3 years, trojans came south bend meet notre dame , first-year head coach charlie weis. irish players entered stadium before game wearing green jerseys, , put crowd frenzy. close game throughout, irish took lead 2 minutes left on brady quinn touchdown run. trojans stormed after 4th , 9 pass matt leinart dwayne jarrett brought ball inside nd 15-yard line. leinart scrambled , tried dive endzone, hit hard short of goal line, , ball knocked out of bounds 7 seconds go. however, clock continued count down, , after hit zero, irish fans began storm field. there no replay in game, @ request of coach pete carroll, after huddling, officials spotted ball on one-yard line , put 7 seconds on clock. on next play, instead of securing tie have resulted in overtime, trojan offense surprised irish running ball. trojan running reggie bush pushed matt leinart, although technically against rules @ time, referees seldom, if ever, made call. weis said hope running mak

1983.E2.80.9395 .E2.80.93 Notre Dame.27s .22Decade of Dominance.22 Notre Dame–USC football rivalry

^ cite error: named reference 2007 nd guide history invoked never defined (see page). ^ cite error: named reference 2006 usc guide history invoked never defined (see page). ^ anderson, dave (1988-11-27). sports of times; lou holtz of notre dame raps gavel again . nytimes.com. retrieved 2008-04-25.  ^ 2007 notre dame media guide: 2007 supplement (page 165) . und.cstv.com. retrieved 2008-04-26.  ^ cite error: named reference fbs past national champions invoked never defined (see page). ^ riled holtz apologizes usc-notre dame brawl . austin-american statesman. 1989-10-22. retrieved 2008-04-26. 

References Sister Rosetta Tharpe

bibliography boyer, horace clarence (1995). how sweet sound: golden age of gospel. elliott , clark. isbn 0-252-06877-7.  heilbut, tony (1997). gospel sound: news , bad times. limelight editions. isbn 0-87910-034-6.  wald, gayle (september 2003). spirituals swing: sister rosetta tharpe , gospel crossover . american quarterly. 55 (3): 387–416.  wald, gayle (2007). shout, sister, shout!: untold story of rock-and-roll trailblazer sister rosetta tharpe. beacon press. isbn 0-8070-0984-9.  white, charles (2003). life , times of little richard: authorised biography. omnibus press. p. 17. 

Desktop APUs List of AMD accelerated processing unit microprocessors

1 desktop apus 1.1 lynx: llano (2011) 1.2 virgo: trinity (2012) 1.3 richland (2013) 1.4 kabini (2014, soc) 1.5 kaveri (2014) 1.6 carrizo (2016) 1.7 bristol ridge (2016) desktop apus lynx: llano (2011) fabrication 32 nm on globalfoundries soi process socket fm1 die size: 228 mm, 1.178 billion transistors cpu cores upgraded architecture known stars (or amd 10h or husky or k10.5) no l3 cache gpu: terascale 2 all , e series models feature redwood-class integrated graphics on die (beavercreek dual-core variants , winterpark quad-core variants). sempron , athlon models exclude integrated graphics. support 4 dimms of ddr3-1866 memory 5 gt/s umi integrated pcie 2.0 controller select models support turbo core technology faster cpu operation when thermal specification permits select models support hybrid graphics technology assist discrete radeon hd 6450, 6570, or 6670 discrete graphics card. similar current hybrid crossfirex technology available in amd 700 , 800 chipset series m

In other media Soder Cola

1 in other media 1.1 films 1.2 video games 1.3 television 1.4 theme parks in other media films signs advertising soder cola can seen in background throughout lego batman movie. video games soder cola appears in dc universe online. drink heals , restores power varying amounts depending on type. many vendors sell them. 2 of same type common reward side missions. mobs uncommonly drop them according mob s level, meaning high level mobs drop high-quality soder cola. numerous billboards appear throughout metropolis , gotham city advertising soda franchise. in gotham city, bane has made drug distribution center out of old soder cola plant. series of health-restorative consumables fall under soder cola franchise. soder cola referenced in batman: arkham origins. there billboards throughout city advertising drink. later batman travels soder cola building mission. drink appears again in batman: arkham knight. television a liter bottle of soder cola seen in justice league unlimited episode questi

Spread Rational trigonometry

1 spread 1.1 calculating spread 1.1.1 trigonometric 1.1.2 vector/slope (two-variable) 1.1.3 cartesian (three-variable) 1.2 spread compared angle 1.3 turn , coturn 1.4 twist spread suppose l1 , 12 intersect @ point a. let c foot of perpendicular b 12. spread s = q/r. spread gives 1 measure separation of 2 lines single dimensionless number in range [0,1] (from parallel perpendicular) euclidean geometry. replaces concept of angle has several differences angle, discussed in section below. spread can have several interpretations. trigonometric (most elementary): sine ratio quadrances in right triangle (left) , therefore equivalent square of sine of angle. viewing side ac part of unit diameter of circle , considering similar triangles (right), spread measured exterior segment, equal 1 half times (1 minus cosine of central angle), twice angle @ a, , haversine. vector: rational function of relative directions (or slopes) of pair of lines meet. cartesian: rational function of 3 co-ordinates use